Name the marked angle in 2 different ways.

Answer:

Step-by-step explanation:

R250:R150:R100 = 5:3:2

The expression 5x^2 - 20x can be factored completely as 5x(x - 4), where 5x is the common factor and (x - 4) is the remaining factor.

To factor the expression 5x^2 - 20x completely, we can look for common factors and apply the distributive property. The given expression has a common factor of 5x, so we can factor it out.

Taking out the common factor, we have:

5x^2 - 20x = 5x(x - 4)

The factor 5x represents the common factor of the terms 5x^2 and -20x. By factoring out 5x, we are left with the expression (x - 4) inside the parentheses.

This means that 5x^2 - 20x can be written as the product of the factors 5x and (x - 4).

To check if the factorization is correct, we can distribute the factors back to the original expression:

5x(x - 4) = 5x * x - 5x * 4 = 5x^2 - 20x

This confirms that the factorization 5x(x - 4) is correct.

Therefore, the expression 5x^2 - 20x can be completely factored as 5x(x - 4).

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The standard form of the given equation is -k² + 7k

Quadratic Equation:

A quadratic equation is a quadratic polynomial in variables of type f(x) = ax2 + bx + c = 0, a, b, c, ε R and a ≠ 0. It is the general form of the quadratic equation. 'a' is called the principal coefficient and 'c' is called the absolute term of f(x). The value of x that satisfies a quadratic equation is the root (α, β) of the quadratic equation.

Standard Form of a Number:

A standard form is a way of writing certain mathematical concepts, such as equations, numbers, and formulas, in a form that follows certain rules. Standard forms are used to concisely represent very large or very small numbers. For example, 4.5 billion years is written as 4.5 billion years. As you can see here, writing a large number like 4.5 billion in its numeric form is not only ambiguous and time consuming, it can add or subtract a few zeros when writing in numeric form. There is a nature. In this case, writing the numbers in standard form can be very helpful. For example, 4,500,000,000 = 4.5 × 109 in normal form. You can write not only numbers but also fractions, equations, formulas, polynomials, etc. in standard form.

Now,

Given that:

c = k - 3

b = k² - 6k -3

Now,

C - B = k - 3 - (k² - 6k -3)

        = k - 3 - k² +6k + 3

        = k - k² + 6k

        = -k² + 7k

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According to the given information, the sample period should be from 2010-2020.

a) Model specification

The model specification based on the scenario above is as follows:

SDF= f(T, TI, NL)

Where: SDF= Sustainable Development Framework

T= Tourism

TI= Technological innovation

NL= National leadership

b) Justification for the selection of the dependent and independent variables model:

Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.

Independent variables:

The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.

The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.

c) Justification for the selection of the sample period:

The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.

Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.

The sample period should be from 2010-2020.

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Based on the fact that Jessica wants to attach ribbons around her wardrobe, the amount more of ribbons that she needs is 5/6 meters of ribbons

Find out the distance wound Jessica's wardrobe:

= 1¹/₃ + ²/₃ + 1¹/₃ + ²/₃

= 58 / 12

= 4 ⁵/₆ meters

The amount more that Jessica needs is therefore:

= 4 ⁵/₆ - 4

= 5/6 meters of ribbons

In conclusion, Jessica needs 5/6 meters of ribbons

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Answer:

up 3 units

Step-by-step explanation:

y = f(x) + C   C > 0 moves it up

We are moving the graph up 3 units

The number of ways that A and B can have subsets is the product of the number of subsets of A and the number of subsets of B, or (2^n) * (2^m) = 2^(n+m).

A set is a collection of distinct objects, and a subset is a set that contains only elements that are also in another set. If set A is a subset of set B, then all elements of A are also elements of B.

The number of subsets of a set with n elements is 2^n. So, if set A has n elements and set B has m elements (where m > n), the number of subsets of A is 2^n and the number of subsets of B is 2^m. The number of ways that A and B can have subsets is the product of the number of subsets of A and the number of subsets of B, or (2^n) * (2^m) = 2^(n+m).

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The answer is B.

The Value iof ∠E in the parallelogram EFGH is 87°

What is parallelogram?

A parallelogram is a basic quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure.

Solution:

We are provided that the Parallelogram is named as EFGH

So, it can be deciphered that E and F are corresponding angles

so, Sum of the Corresponding Angles of Parallelogram is 180°

E = 2x + 3

F = 3x - 33

E + F = 180

2x + 3 + 3x - 33 = 180

5x - 30 = 180

5x = 210

x = 42°

∠E = 2*42 + 3 = 87°

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On a graph, the absolute value of a number is always non-negative.

The absolute value of a number is defined as the distance of that number from zero on the number line. Since the distance can never be negative, the absolute value of a number is always non-negative.

This is reflected in the graph of an absolute value function. The graph of an absolute value function, |x| is a V-shape that opens upward, with the vertex of the V being the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line. The coordinates of the vertex (0,0) and the graph is always non-negative.

It's important to note that although the absolute value is always non-negative on a graph, the input value (x) can be both positive and negative. The output of the absolute value function (|x|) will always be positive.

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Using Pythagorean Theorem, the length of the line segment from (-3, 10) to (4, -1) is 13 units.

Pythagorean theorem describes the relationship between the sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two other side.

c² = a² + b²

Let a = vertical distance between the two points

b = horizontal distance between the two points

c = distance between the two points / length of line segment

Hence, c² = (|y₂ - y₁|)² + (|x₂ - x₁|)².

Substitute the values of x and y and solve for c.

c² = (|y₂ - y₁|)² + (|x₂ - x₁|)²

c² = (|-1 - 10|)² + (|4 - -3|)²

c² = (|-11|)² + (|7|)²

c² = 11² + 7²

c² = 121 + 49

c² = 170

c = 13.04

length of line segment ≅ 13 units

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The first 3 terms of the sequence are 21, 24 and 29

From the question, we have the following parameters that can be used in our computation:

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

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Answer:

126

Step-by-step explanation:

Perimeter=2(l+w)

50/2=25.....25-w

25-7=18

Area= lxw

18x7=126

The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.

Volume is the measure of the amount of 3-dimensional space occupied by an object or substance. It is usually measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in mathematics, physics, chemistry, and engineering, and is used to calculate the amount of material needed for a given project.

The volume of the box can be calculated by multiplying the area of the base with the height of the box. The area of the base is 58 cm² and the height of the box is x - 2 cm. Therefore, the volume of the box can be expressed as:
Volume = 58 cm² x (x - 2 cm)
     = 58 cm³
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.

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F distribution is used with the global test of the regression model to reject the null hypothesis.

The hypothesis test will be conducted using a novel distribution. After the English statistician Sir Ronald Fisher, it is known as the F distribution. A ratio, the F statistic is (a fraction). One set of degrees of freedom is for the denominator, and the other set is for the numerator.

According to the null hypothesis, all group population means are equal. Because it is assumed that the populations are normal and that they have similar variances, the equal means hypothesis indicates that the populations have the same normal distribution. All groups are samples from populations with the same normal distribution, according to the null hypothesis. According to the alternative theory, at least two of the sample groups are drawn from populations with various normal distributions.

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Answer:

undefined

Step-by-step explanation:

y2 -y1

______

x2 -x1

27 - 2

_____

9-9

25

__

0

The line is a vertical line, thus, the slope is not defined.

If we know that a line passes through two points (a, b) and (c, d), then the slope is given by the expression:

slope = (d - b)/(c - a)

Here we have the two points (9, 2) and (9, 27)

So the slope is:

slope = (27 -  2)/(9 - 9)

That tends to infinity, and this happens because this is a vertical line. So the slope is undefined.

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Step-by-step explanation:

the coordinates of the quadrilateral WXYZ after reflected across the y-axis:

W' (3, 4)

X' (-2, 8)

Y' (-4, -4)

Z' (3, -4)

Answer:

Step-by-step explanation:

Answer:

37.1

Step-by-step explanation:

Hope this is the right answer.

(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

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Answer:

12n

Step-by-step explanation:

5 x 2n = 10n +2 = 12n

Answer:

Step-by-step explanation:

Answer:

4:4:4

Step-by-step explanation:

1/3 of the beet was replaced with wheat => 6 x 1/3 = 2

The new ratio will be 4 : (2+2) : (6-2) = 4:4:4

the mathematical statement "a number n increased by 16" is equivalent to the algebraic expression:

n + 16

Here we have a mathematical statement which says "a number n increased by 16"

An "increase" is a sum. So the mathematical expression will just be the addition between a number (which we will denote with the variable n) and 16.

n + 16.

Concluding, the mathematical statement "a number n increased by 16" is equivalent to the algebraic expression:

n + 16

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Equation: y * 5 = 85

In this equation, 'y' represents the number of learners in class 9T, and '5' represents the number of pencils each learner receives. The equation states that the product of the number of learners (y) and the number of pencils each learner receives (5) is equal to the total number of pencils (85) that Mrs. Leclerc shares among the learners.

This equation can be used to solve for the value of 'y' by dividing both sides of the equation by 5. By doing so, we can determine the number of learners in class 9T based on the given information about the number of pencils shared.

For example, if we divide 85 by 5, the result is 17. Therefore, there are 17 learners in class 9T.

In summary, the equation y * 5 = 85 represents the situation where Mrs. Leclerc shares 85 pencils between the learners in class 9T, with each learner receiving 5 pencils. By solving the equation, we can find the number of learners in the class, which in this case is 17.

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Answer:

5xy (3x - 5y + 15xy)

Step-by-step explanation:

Ahora, si quiero tomar factores comunes, debo buscar algo que divida todos los términos de la expresión.

Este término que va a dividir todos los términos de la expresión es 5xy

Por lo tanto, para factorizar 15x2y - 25xy2 + 75x2y2

Tengo;

5xy (3x - 5y + 15xy)

The determinant of the given matrix using expansion by cofactors is -29640.  In expansion by cofactors, the determinant of an n x n matrix can be computed by expanding along any row or column.

Let's expand along the first row of the given matrix.

The cofactor of each element in the first row is found by taking the determinant of the submatrix formed by excluding the row and column of that element, and multiplying it by the sign \((-1)^{(i+j)\), where i and j are the row and column indices of the element.

For example, the cofactor of the element w is determined by taking the determinant of the submatrix:

10 -18 32

32 22 -35

The determinant of this 2 x 2 submatrix is (10 * (-35)) - (32 * 22) = -1050 - 704 = -1754. Multiplying this by the sign (-1)^(1+1) = 1 gives us the cofactor of w as -1754.

Repeating this process for each element in the first row, we have:

Cofactor of w = -1754

Cofactor of x = -2684

Cofactor of y = -1020

Cofactor of z = -2182

Finally, we calculate the determinant by multiplying each element in the first row by its corresponding cofactor and summing them up:

w * (-1754) + x * (-2684) + y * (-1020) + z * (-2182) = -29640

Therefore, the determinant of the given matrix using expansion by cofactors is -29640.

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